Mist + dof + alpha in cycles
This is a tricky one, because you're going to deal with two separate issues that clash with each other.

As @cegaton suggested, volumetrics could make things easier for you, but if you need to solve it with compositing alone anyway, there's a couple of things you need to know:


The mist pass can help you but ONLY if you intend to composite the pass over the composited plate (no alpha channel). Since it's antialiased, compositing a mist pass over an image with alpha channel will result in color contamination in AA pixels and pixels convoluted by the DoF effect, as you experienced in your tests.
The Z buffer in Blender plays really bad with cycles DoF. I dare to say that it's completely useless when DoF is used. Just normalize it and examine it with the viewer, the sampling in the defocused areas makes it really inadequate for compositing, unless you're going to use an insanely high number of samples, which beats the purpose of not using volumetrics.
Alpha channel is also tricky when used with depth effects because alpha compositing is intended for blending a foreground plate over a background plate, not multiple planes in different depths.


With that in mind it becomes obvious that there isn't a silver-bullet solution to composite this kind of imagery in one single pass (unless you work on the composited beauty pass directly, without alpha channel).

If you need to produce layers to be composited using DoF and mist, you'll have to deal with the aliased Z pass and cut slices out of your scene's depth to apply the DoF effect in post without producing bleeds and artifacts.
It's a somewhat complex and tedious process and you'll have to evaluate whether it is worth to invest so much time and effort in compositing to spare yourself some extra minutes of rendering.